For genetic engineering which entrance we should give JEE or NEET ?and what higher studies we are expected to do .

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Hai injila shakeel,
The course ur asking is an specialisation.
First you should study and graduation From IIT then take IIT-JEE Exam and take up B.Tech in Biotechnology or Biomedical Engineering programmes.
Choose IISER centers for biology based courses as second option.
The Indian Institutes of Technology Madras and Kharagpur Locations are best for the core Biology based (IITs).
They dont offer B.Tech. course in Genetic Engineering, but Instead, Biotechnology and Biochemical Engineering programmes can enroled into.
IIT, Madras conducts B.Tech. and five-year dual-degree M.Tech. programmes in Biotechnology.